Is income earned from a job obtained by paying a bribe considered unlawful (haram), and is sincere repentance sufficient to rectify this sin, or must one leave the job?

If you are performing your new job to the best of your ability, then there is no blame upon you for remaining in it and benefiting from its wage. Your remorse is repentance, so resolve not to return to such an act again, seek Allah's forgiveness, and draw closer to Him through righteous deeds, for good deeds erase bad ones. You are not obligated to leave the job if you are performing it well.